Engineering task and calculation objective
The BIFL module balances humid air during desuperheating and condensation. A typical application is the compressed-air aftercooler downstream of a compressor: ambient air with a known relative humidity φ is drawn in, compressed, enters the cooler hot, and is cooled below its dew point – condensate forms, which the downstream separator must remove. Air coolers in drying plants, air-conditioning processes, and process air systems can also be balanced with it.
From the mass flow or standard volume flow of the dry air, the intake state (temperature ϑ0, pressure p0, relative humidity φ), and the inlet and outlet states of the cooler, the module calculates the dew point temperature ϑTau at the operating pressure, the condensed water quantity mkond, and the heat flows split into desuperheating QEnth (cooling down to the dew point) and condensation QKond (cooling with water dropout). The sum QGes is the design duty of the cooler.
The split into a desuperheating zone and a condensation zone is essential for heat exchanger design, because the heat transfer conditions in the condensation zone differ markedly from dry gas cooling. The basis is the state equations of humid air (Mollier h-x systematics) together with the saturation vapour pressure of water.
Calculation workflow
- Define the intake state and air quantity: From the temperature ϑ0, pressure p0, and relative humidity φ of the intake air, the absolute moisture content x of the air is determined. The mass flow of dry air mtr – optionally derived from the standard volume flow Vn,tr – is the reference quantity of the entire balance, because it remains constant through the process.
- Calculate the dew point temperature at the operating pressure: At the elevated pressure pe, the water vapour partial pressure rises proportionally; the dew point temperature ϑTau follows from the condition that the partial pressure reaches the saturation vapour pressure. If the cooler outlet temperature ϑa lies below it, condensate forms.
- Determine the condensed water quantity: At the outlet, the air is saturated; its residual moisture content follows from the saturation vapour pressure at ϑa and the outlet pressure pa. The difference in moisture contents times the dry air mass flow yields the condensed water quantity mkond as well as the mass flows of the humid air at inlet and outlet.
- Balance the heat flows: Via the enthalpy of humid air, the heat flow is split into desuperheating QEnth (from ϑe down to ϑTau, without phase change) and condensation QKond (from ϑTau down to ϑa, including the enthalpy of vaporization of the water dropping out); the sum QGes is the required cooling duty.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Luft | Luft | kg/s |
| Luft | Luft | % |
| Luft | Luft | °C |
| Luft | Luft | °C |
| Luft | Luft | °C |
| Luft | Luft | Pa |
| Luft | Luft | Pa |
| Luft | Luft | Pa |
| Wassers | Wassers | Pa |
| Wassers | Wassers | °C |
| Wassers | Wassers | °C |
| Luft | Luft | m³/s |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| ein | ein | kg/s |
| aus | aus | kg/s |
| Wassermenge | Wassermenge | kg/s |
| Tautemperatur | Tautemperatur | °C |
| Kondensationswärmestrom | Kondensationswärmestrom | W |
| Enthitzungswärmestrom | Enthitzungswärmestrom | W |
| Wärmestrom | Wärmestrom | W |
| Wassers | Wassers | kg/s |
| Tautemp. | Tautemp. | °C |
Worked example
A compressed-air aftercooler is to be balanced – a worked example of a humid air calculation. A compressor draws in ambient air and compresses it to 3.0 bar (absolute). The air enters the aftercooler at 120 °C and is cooled to 25 °C (pressure drop neglected). Required: dew point temperature, condensate quantity, and cooling duty, split into desuperheating and condensation.
Given values
| Mass flow of dry air mtr | 0.5 kg/s |
| Intake state ϑ0 / p0 / φ | 20 °C / 1.0 bar / 60 % |
| Cooler inlet temperature ϑe | 120 °C |
| Cooler outlet temperature ϑa | 25 °C |
| Operating pressure pe ≈ pa | 3.0 bar (absolute) |
Solution
Moisture content of the intake air
Saturation vapour pressure at 20 °C (Magnus formula): ps(20 °C) ≈ 2,333 Pa. With φ = 0.60 and p0 = 100,000 Pa, the moisture content follows as
x0 = 0.622 · φ·ps / (p0 − φ·ps) = 0.622 · 1,400 / (100,000 − 1,400) ≈ 8.8 g of water per kg of dry air.
This moisture content remains unchanged during compression.
Dew point temperature at 3.0 bar
The water vapour partial pressure at the operating pressure is pD = x0·p / (0.622 + x0) = 0.00883 · 300,000 / 0.6308 ≈ 4,199 Pa. Inverting the saturation curve gives
ϑTau ≈ 29.9 °C — so the air already starts to condense just below 30 °C.
Condensate quantity
At the outlet (25 °C, 3.0 bar) the air is saturated: ps(25 °C) ≈ 3,160 Pa, hence xs = 0.622 · 3,160 / (300,000 − 3,160) ≈ 6.6 g/kg.
mkond = mtr · (x0 − xs) = 0.5 kg/s · (8.83 − 6.62) g/kg ≈ 1.10 g/s ≈ 4.0 kg/h of condensate.
Heat flows
With the enthalpy of humid air h1+x = 1.006·ϑ + x·(2501 + 1.86·ϑ) in kJ/kg of dry air:
Desuperheating 120 °C → 29.9 °C: QEnth = 0.5 · (144.8 − 52.6) ≈ 46.1 kW
Condensation 29.9 °C → 25 °C (incl. enthalpy of vaporization, minus the enthalpy of the drained condensate): QKond ≈ 5.2 kW
QGes = QEnth + QKond ≈ 51.3 kW.
Result
| Dew point temperature at 3.0 bar | ≈ 29.9 °C |
| Condensed water quantity mkond | ≈ 4.0 kg/h |
| Heat flow desuperheating QEnth | ≈ 46.1 kW |
| Heat flow condensation QKond | ≈ 5.2 kW |
| Total cooling duty QGes | ≈ 51.3 kW |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why does water condense out when air is compressed, even though the air quantity stays the same?
The absolute moisture content does not change during compression, but the partial pressure of the water vapour rises in proportion to the total pressure. At 3 bar, the dew point of the same air is therefore significantly higher than at 1 bar – air that would only condense at 12 °C at ambient pressure reaches its dew point at about 30 °C after compression. If the aftercooler cools below that, condensate inevitably forms.
Why is the balance referred to the mass flow of dry air?
The mass flow of the humid air changes between inlet and outlet because of the condensate dropping out; the dry air fraction, on the other hand, remains constant. All moisture contents x and specific enthalpies h are therefore referred to 1 kg of dry air – this eliminates the varying water quantity from the balance and keeps the calculation closed.
Why are desuperheating and condensation reported separately?
In the desuperheating zone, cooling is dry; the heat transfer corresponds to gas cooling. From the dew point on, water condenses on the cooling surface, heat transfer improves considerably, and per kelvin of cooling much more heat must be removed because of the enthalpy of vaporization. For the surface allocation and the coolant routing of the heat exchanger, both zones must be considered separately.
Does the calculation also apply to other gas-vapour mixtures?
The systematics (moisture content, partial pressure, dew point) are transferable, but the property data are not: the module uses the saturation curve of water and the gas constant and heat capacity of air. For mixtures of process gases with other condensates, separate vapour pressure curves and property data are required. In addition, the ideal gas approach applies; at very high pressures, real mixtures deviate increasingly.